Question

For the demand function q equals Upper D (p )equals 357 minus p​, find the following. ​a) The elasticity ​b) The elasticity at pequals89​, stating whether the demand is​ elastic, inelastic or has unit elasticity ​c) The​ value(s) of p for which total revenue is a maximum​ (assume that p is in​ dollars)

Answer 1

The required elasticity is
`E_p=(p)/(357-p)`.

The demand is inelastic.

The required value of p for which total revenue is maximum is 178.5

Explanation:

Consider the provided function.

`D_p= 357-p`

`D_p=q= 357-p`

Part (A) The elasticity ​

The elasticity of demand is:
`E_p=(p)/(q) \cdot (dq)/(dp)`

`(dq)/(dp)=-1`

But elasticity is always positive therefore,

`E_p=(p)/(357-p)`

Hence, the required elasticity is
`E_p=(p)/(357-p)`.

Part (​b) The elasticity at p=89​, stating whether the demand is​ elastic, inelastic or has unit elasticity.

Substitute p=89 in above elasticity formula.

`E_(89)=(89)/(357-89)`

`E_(89)=(89)/(268)`

The above value is less than 1, therefore the demand is inelastic.

Part (C) The​ value(s) of p for which total revenue is a maximum​ (assume that p is in​ dollars).

For maximum revenue substitute E=1.

`1=(p)/(357-p)`

`357-p=p`

`2p=357`

`p=178.5`

Hence, the required value of p for which total revenue is maximum is 178.5